Rima is a distinctive girls' name in United States, ranking #5600 in 2014 with 24 recorded births. The name reached its all-time peak in 2015 with 38 births ranking #3973. Since 1996, the popularity has increased by 20.0%. In 2014, approximately 1 in every 74,414 girls born was named Rima. RISING Recent data shows the name is currently rising.